Theorems · Theorem · ring theory
isSimpleModule_iff_finrank_eq_one
∀ {R : Type u_1} {M : Type u_2} [inst : DivisionRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],
IsSimpleModule R M ↔ Module.finrank R M = 1- Defined in
- Mathlib.RingTheory.SimpleModule.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- DivisionRingstatement and proof · cited by 1,062
- IsSimpleModulestatement and proof · cited by 114
- exists_neproof · cited by 101
- isSimpleModule_iffproof · cited by 12
- finrank_eq_one_iff_of_nonzero'proof · cited by 11
- IsSimpleModule.nontrivialproof · cited by 8
- IsSimpleModule.toSpanSingleton_surjectiveproof · cited by 4
- is_simple_module_of_finrank_eq_oneproof · cited by 2
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